..
.
..
.
..
.
..
.
SLIDES BY
John Loucks
St. Edward’s
University
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied
or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 1
Chapter 2, Part B
Descriptive Statistics:
Tabular and Graphical Displays
Summarizing Data for Two Variables
Using Tables
Summarizing Data for Two Variables
Using Graphical Displays
Data Visualization: Best Practices in Creating
Effective Graphical Displays
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied
or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 2
Summarizing Data for Two Variables
Using Tables
Thus far we have focused on methods that are used
to summarize the data for one variable at a time.
Often a manager is interested in tabular and
graphical methods that will help understand the
relationship between two variables.
Crosstabulation is a method for summarizing the
data for two variables.
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied
or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 3
Crosstabulation
A crosstabulation is a tabular summary of data for
two variables.
Crosstabulation can be used when:
• one variable is categorical and the other is
quantitative,
• both variables are categorical, or
• both variables are quantitative.
The left and top margin labels define the classes for
the two variables.
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied
or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 4
Crosstabulation
Example: Finger Lakes Homes
The number of Finger Lakes homes sold for each
style and price for the past two years is shown below.
quantitative
categorical
variable
variable
Home Style
Price
Colonial Log Split A-Frame Total
Range
< $250,000
> $250,000
18
12
6
14
19
16
12
3
55
Total
30
20
35
15
100
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied
or duplicated, or posted to a publicly accessible website, in whole or in part.
45
Slide 5
Crosstabulation
Example: Finger Lakes Homes
Insights Gained from Preceding Crosstabulation
•
The greatest number of homes (19) in the sample
are a split-level style and priced at less than
$250,000.
•
Only three homes in the sample are an A-Frame
style and priced at $250,000 or more.
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied
or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 6
Crosstabulation
Example: Finger Lakes Homes
Frequency
distribution
for the
price range
variable
Home Style
Log Split A-Frame
Price
Range
Colonial
< $250,000
> $250,000
18
12
6
14
19
16
12
3
55
Total
30
20
35
15
100
Total
45
Frequency distribution for
the home style variable
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied
or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 7
Crosstabulation: Row or Column Percentages
Converting the entries in the table into row
percentages or column percentages can provide
additional insight about the relationship between
the two variables.
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied
or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 8
Crosstabulation: Row Percentages
Example: Finger Lakes Homes
Price
Range
Colonial
< $250,000
> $250,000
32.73
26.67
Home Style
Log Split A-Frame
10.91
31.11
34.55
35.56
21.82
6.67
Total
100
100
Note: row totals are actually 100.01 due to rounding.
(Colonial and > $250K)/(All > $250K) x 100 = (12/45) x 100
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied
or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 9
Crosstabulation: Column Percentages
Example: Finger Lakes Homes
Price
Range
Colonial
< $250,000
> $250,000
60.00
40.00
30.00
70.00
54.29
45.71
80.00
20.00
Total
100
100
100
100
Home Style
Log Split A-Frame
(Colonial and > $250K)/(All Colonial) x 100 = (12/30) x 100
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied
or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 10
Crosstabulation: Simpson’s Paradox
Data in two or more crosstabulations are often
aggregated to produce a summary crosstabulation.
We must be careful in drawing conclusions about the
relationship between the two variables in the
aggregated crosstabulation.
In some cases the conclusions based upon an
aggregated crosstabulation can be completely
reversed if we look at the unaggregated data. The
reversal of conclusions based on aggregate and
unaggregated data is called Simpson’s paradox.
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied
or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 11
Summarizing Data for Two Variables
Using Graphical Displays
In most cases, a graphical display is more useful than
a table for recognizing patterns and trends.
Displaying data in creative ways can lead to powerful
insights.
Scatter diagrams and trendlines are useful in
exploring the relationship between two variables.
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied
or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 12
Scatter Diagram and Trendline
A scatter diagram is a graphical presentation of the
relationship between two quantitative variables.
One variable is shown on the horizontal axis and
the other variable is shown on the vertical axis.
The general pattern of the plotted points suggests
the overall relationship between the variables.
A trendline provides an approximation of the
relationship.
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied
or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 13
Scatter Diagram
A Positive Relationship
y
x
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied
or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 14
Scatter Diagram
A Negative Relationship
y
x
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied
or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 15
Scatter Diagram
No Apparent Relationship
y
x
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied
or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 16
Scatter Diagram
Example: Panthers Football Team
The Panthers football team is interested in
investigating the relationship, if any, between
interceptions made and points scored.
x = Number of
Interceptions
1
3
2
1
3
y = Number of
Points Scored
14
24
18
17
30
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied
or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 17
Scatter Diagram and Trendline
Number of Points Scored
y
35
30
25
20
15
10
5
0
0
1
x
2
3
4
Number of Interceptions
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied
or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 18
Example: Panthers Football Team
Insights Gained from the Preceding Scatter Diagram
•
The scatter diagram indicates a positive relationship
between the number of interceptions and the
number of points scored.
•
Higher points scored are associated with a higher
number of interceptions.
• The relationship is not perfect; all plotted points in
the scatter diagram are not on a straight line.
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied
or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 19
Side-by-Side Bar Chart
A side-by-side bar chart is a graphical display for
depicting multiple bar charts on the same display.
Each cluster of bars represents one value of the
first variable.
Each bar within a cluster represents one value of
the second variable.
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied
or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 20
Side-by-Side Bar Chart
Finger Lake Homes
20
18
Frequency
16
14
< $250,000
> $250,000
12
10
8
6
4
2
Colonial
Log
Split-Level A-Frame
Home Style
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied
or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 21
Stacked Bar Chart
A stacked bar chart is another way to display and
compare two variables on the same display.
It is a bar chart in which each bar is broken into
rectangular segments of a different color.
If percentage frequencies are displayed, all bars
will be of the same height (or length), extending to
the 100% mark.
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied
or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 22
Stacked Bar Chart
Finger Lake Homes
40
36
Frequencies
displayed
Frequency
32
28
< $250,000
> $250,000
24
20
16
12
8
4
Colonial
Log
Split
A-Frame
Home Style
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied
or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 23
Percentage Frequency
Stacked Bar Chart
Finger Lake Homes
100
90
Percentage
frequencies
displayed
80
70
< $250,000
> $250,000
60
50
40
30
20
10
Colonial
Log
Split
A-Frame
Home Style
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied
or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 24
Data Visualization: Best Practices
in Creating Effective Graphical Displays
Data visualization describes the use of graphical
displays to summarize and present information
about a data set.
The goal is to communicate as effectively and clearly
as possible the key information about the data.
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied
or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 25
Creating Effective Graphical Displays
Creating effective graphical displays is as much art
as it is science.
Here are some guidelines . . .
Give the display a clear and concise title.
Keep the display simple.
Clearly label each axis and provide the units of
measure.
If colors are used, make sure they are distinct.
If multiple colors or lines are used, provide a
legend.
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied
or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 26
Choosing the Type of Graphical Display
Displays used to show the distribution of data:
Bar Chart to show the frequency distribution or relative
frequency distribution for categorical data
Pie Chart
to show the relative frequency or percent
frequency for categorical data
Dot Plot
to show the distribution for quantitative data
over the entire range of the data
Histogram
to show the frequency distribution for
quantitative data over a set of class intervals
Stem-and-Leaf Display
to show both the rank order and
shape of the distribution for
quantitative data
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied
or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 27
Choosing the Type of Graphical Display
Displays used to make comparisons:
Side-by-Side Bar Chart
Stacked Bar Chart
to compare two variables
to compare the relative frequency or
percent frequency of two categorical
variables
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied
or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 28
Choosing the Type of Graphical Display
Displays used to show relationships:
Scatter Diagram
Trendline
to show the relationship between two
quantitative variables
to approximate the relationship of data in a
scatter diagram
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied
or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 29
Data Dashboards
A data dashboard is a widely used data
visualization tool.
It organizes and presents key performance indicators
(KPIs) used to monitor an organization or process.
It provides timely, summary information that is easy
to read, understand, and interpret.
Some additional guidelines include . . .
Minimize the need for screen scrolling.
Avoid unnecessary use of color or 3D.
Use borders between charts to improve
readability.
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied
or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 30
Data Dashboard Example
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied
or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 31
Tabular and Graphical Displays
Data
Categorical Data
Tabular
Displays
• Frequency
Distribution
• Rel. Freq. Dist.
• Percent Freq.
Distribution
• Crosstabulation
Graphical
Displays
• Bar Chart
• Pie Chart
• Side-by-Side
Bar Chart
• Stacked
Bar Chart
Quantitative Data
Tabular
Displays
• Frequency
Distribution
• Rel. Freq. Dist.
• % Freq. Dist.
• Cum. Freq. Dist.
• Cum. Rel. Freq.
Distribution
• Cum. % Freq.
Distribution
• Crosstabulation
Graphical
Displays
• Dot Plot
• Histogram
• Stem-andLeaf Display
• Scatter
Diagram
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied
or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 32
End of Chapter 2, Part B
© 2015 Cengage Learning. All Rights Reserved. May not be scanned, copied
or duplicated, or posted to a publicly accessible website, in whole or in part.
Slide 33
